陳思寬王之彥臺灣大學：陳俊英Chen, Jung-YingJung-YingChen2007-11-282018-06-292007-11-282018-06-292005http://ntur.lib.ntu.edu.tw//handle/246246/60400There are two contributions in this article. The first is to offer a general version of martingale pricing method to value the class of options whose payoffs depend on historical prices of multiple assets. The second is to derive a Black-Scholes-type closed form formula of options on the maximum or minimum of multiple assets’ discrete lookback prices. In addition, the formula is able to degenerate to the one for options on the maximum or minimum of multiple assets in Johnson (1987) and the one for discrete lookback option for one asset in Heynen and Kat (1995).1 Introduction 4 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Review of Literature 6 2.1 Lookback Options . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Reset Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Rainbow Options . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Valuation Model 8 3.1 Notations and Assumptions . . . . . . . . . . . . . . . . . . . 8 3.2 Fixed Strike Calls on the Maximum . . . . . . . . . . . . . . . 9 3.3 Fixed Strike Calls on the Minimum . . . . . . . . . . . . . . . 11 4 Applications 13 4.1 Options on the Maximum of Several Assets . . . . . . . . . . . 13 4.2 Discrete Lookback Options of One Asset with Fixed Strike . . 14 5 Numerical Results 17 5.1 Different Number of Assets and Monitoring Frequencies . . . . 17 5.2 Other Characteristics . . . . . . . . . . . . . . . . . . . . . . . 19 5.3 Delta and Gamma . . . . . . . . . . . . . . . . . . . . . . . . 23 6 Conclusion 27 A Proofs and Derivations 30 A.1 Girsanov Theorem . . . . . . . . . . . . . . . . . . . . . . . . 30 A.2 Derivations of Formulae . . . . . . . . . . . . . . . . . . . . . 32 A.3 Delta and Gamma . . . . . . . . . . . . . . . . . . . . . . . . 34856065 bytesapplication/pdfen-US離散回顧選擇權多資產極值選擇權lookback optionmaximum or minimum of multiple assetsthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/60400/1/ntu-94-R91724090-1.pdf